Chapter 2: Spatial Concepts and Data Models 2.1 Introduction 2.2 Models of Spatial Information 2.3 Three-Step Database Design 2.4 Extending ER with Spatial Concepts 2.5 Summary - PowerPoint PPT Presentation

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Chapter 2: Spatial Concepts and Data Models 2.1 Introduction 2.2 Models of Spatial Information 2.3 Three-Step Database Design 2.4 Extending ER with Spatial Concepts 2.5 Summary

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Title: Chapter 2: Spatial Concepts and Data Models 2.1 Introduction 2.2 Models of Spatial Information 2.3 Three-Step Database Design 2.4 Extending ER with Spatial Concepts 2.5 Summary


1
Chapter 2 Spatial Concepts and Data Models 2.1
Introduction 2.2 Models of Spatial
Information 2.3 Three-Step Database Design 2.4
Extending ER with Spatial Concepts 2.5 Summary
2
Learning Objectives
  • Learning Objectives (LO)
  • LO1 Understand concept of data models
  • What is a data model?
  • Why use data models?
  • LO2 Understand the models of spatial
    information
  • LO3 Understand the 3-step design of databases
  • LO4 Learn about the trends in spatial data
    models
  • Mapping Sections to learning objectives
  • LO2 - 2.1
  • LO3 - 2.2
  • LO4 - 2.3, 2.4

3
What is a Data Model?
  • What is a model? (Dictionary meaning)
  • A set of plans (blueprint drawing) for a
    building
  • A miniature representation of a system to analyze
    properties of interest
  • What is Data Model?
  • Specify structure or schema of a data set
  • Document description of data
  • Facilitates early analysis of some properties,
    e.g. querying ability, redundancy, consistency,
    storage space requirements, etc.
  • Examples
  • GIS organize spatial set as a set of layers
  • Databases organize dataset as a collection of
    tables

4
Why Data Models?
  • Data models facilitate
  • Early analysis of properties, e.g. storage cost,
    querying ability, ...
  • Reuse of shared data among multiple applications
  • Exchange of data across organization
  • Conversion of data to new software / environment
  • Example- Y2K crisis for year 2000
  • Many computer software systems were developed
    without well-defined data models in 1960s and
    1970s. These systems used a variety of data
    models for representing time and date. Some of
    the representations used two digits to represent
    years. In late 1990s, people worried that the 2
    digit representation of year may lead to
    errorneous behaviour. For example age of a person
    born in 1960 (represented as 60) in year 2000
    (represented as 00) may appear negative and may
    be flagged as illegal data item. A large amount
    of effort and resources (hundreds of Billions of
    dollars) was spent in revising the software.
  • Proper use of data model may have significantly
    reduced the costs. If time and date were modeled
    as abstract data types in a software, only a
    small portion of the software implementing the
    date ADT had to be reviewed and revised.

5
Types of Data Models
  • Two Types of data models
  • Generic data models
  • Developed for business data processing
  • Support simple abstract data types (ADTs), e.g.
    numbers, strings, date
  • Not convenient for spatial ADTs, e.g. polygons
  • Recall a polygon becomes dozens of rows in 3
    tables (Fig. 1.4, pp. 8)
  • Need to extend with spatial concepts, e.g. ADTs
  • Application Domain specific, e.g. spatial models
  • Set of concepts developed in Geographic Info.
    Science
  • Common spatial ADTs across different GIS
    applications
  • Plan of Study
  • First study concepts in spatial models
  • Then study generic model
  • Finally put the two together

6
Learning Objectives
  • Learning Objectives (LO)
  • LO1 Understand concept of data models
  • LO2 Understand the models of spatial
    information
  • Field based model
  • Object based model
  • LO3 Understand the 3-step design of databases
  • LO4 Learn about the trends in spatial data
    models
  • Mapping Sections to learning objectives
  • LO2 - 2.1
  • LO3 - 2.2
  • LO4 - 2.3, 2.4

7
2.1 Models of Spatial Information
  • Two common models
  • Field based
  • Object based
  • Example Forest stands
  • Fig. 2.1
  • (a) forest stand map
  • (b) Object view has 3 polygons
  • (c ) Field view has a function

8
2.1.1 Field based Model
  • Three main concepts
  • Spatial Framework is a partitioning of space
  • e.g., Grid imposed by Latitude and Longitude
  • Field Functions
  • f Spatial Framework ? Attribute Domain
  • Field Operations
  • Examples, addition() and composition(o).

9
Types of Field Operations
  • Local value of the new field at a given location
    in the spatial frame-work depends only on the
    value of the input field at that location(e.g.,
    Thresholding)
  • Focalvalue of the resulting field at a given
    location depends on the values that the input
    field assumes in a small neighborhood of the
    location(e.g., Gradient)
  • ZonalZonal operations are naturally associated
    with aggregate operators or the integration
    function. An operation that calculates the
    average height of the trees for each species is a
    zonal operation.
  • Exercise Classify following operations on
    elevation field
  • (I) Identify peaks (points higher than its
    neighbors)
  • (II) Identify mountain ranges (elevation over
    2000 feet)
  • (III) Determine average elevation of a set of
    river basins

10
2.1.2 Object Model
  • Object model concepts
  • Objects distinct identifiable things relevant to
    an application
  • Objects have attributes and operations
  • Attribute a simple (e.g. numeric, string)
    property of an object
  • Operations function maps object attributes to
    other objects
  • Example from a roadmap
  • Objects roads, landmarks, ...
  • Attributes of road objects
  • spatial location, e.g. polygon boundary of
    land-parcel
  • non-spatial name (e.g. Route 66), type (e.g.
    interstate, residential street), number of lanes,
    speed limit,
  • Operations on road objects determine center
    line, determine length, determine intersection
    with other roads, ...

11
Classifying Spatial objects
  • Spatial objets are spatial attributes of
    general objects
  • Spatial objects are of many types
  • Simple
  • 0- dimensional (points), 1 dimensional (curves),
    2 dimensional (surfaces)
  • Example given at the bottom of this slide
  • Collections
  • Polygon collection (e.g. boundary of Japan or
    Hawaii),
  • See more complete list in Figure 2.2

Spatial Object Types Example Object Dimension
Point City 0
Curve River 1
Surface Country 2
12
Spatial Object Types in OGIS Data Model
Fig 2.2 Each rectangle shows a distinct spatial
object type
13
Classifying Operations on spatial objects in
Object Model
  • Classifying operations (Tables 2.1, 2.2, pp.
    29-31)
  • Set based 2-dimensional spatial objects (e.g.
    polygons) are sets of points
  • a set operation (e.g. intersection) of 2
    polygons produce another polygon
  • Topological operations Boundary of USA touches
    boundary of Canada
  • Directional New York city is to east of Chicago
  • Metric Chicago is about 700 miles from New York
    city.
  • Q? Identify classes of spatial operations not
    listed in this slide.

Set theory based Union, Intersection, Containment,
Toplogical Touches, Disjoint, Overlap, etc.
Directional East,North-West, etc.
Metric Distance
14
Topological Relationships
  • Topological Relationships
  • invariant under elastic deformation (without
    tear, merge).
  • Two countries which touch each other in a planar
    paper map will continue to do so in spherical
    globe maps.
  • Topology is the study of topological
    relationships
  • Example queries with topological operations
  • What is the topological relationship between two
    objects A and B ?
  • Find all objects which have a given topological
    relationship to object A ?

15
Topological Concepts
  • Interior, boundary, exterior
  • Let A be an object in a Universe U.

U
A
  • Question Define Interior, boundary, exterior on
    curves and points.

16
Nine-Intersection Model of Topological
Relationships
  • Many toplogical Relationship between A and B can
    be
  • specified using 9 intersection model
  • Examples on next slide
  • Nine intersections
  • intersections between interior, boundary,
    exterior of A, B
  • A and B are spatial objects in a two dimensional
    plane.
  • Can be arranged as a 3 by 3 matrix
  • Matrix element take a value of 0 (false) or 1
    (true).
  • Q? Determine the number of many distinct 3 by 3
    boolean matrices .

17
Specifying topological operation in
9-Intersection Model
Fig 2.3 9 intersection matrices for a few
topological operations
Question Can this model specify topological
operation between a polygon and a curve?
18
Using Object Model of Spatial Data
  • Object model of spatial data
  • OGIS standard set of spatial data types and
    operations
  • Similar to the object model in computer software
  • Easily used with many computer software systems
  • Programming languages like Java, C, Visual
    basic
  • Example use in a Java program is in section 2.1.6
  • Post-relational databases, e.g. OODBMS, ORDBMS
  • Example usage in chapter 3 through 6

19
Learning Objectives
  • Learning Objectives (LO)
  • LO1 Understand concept of data models
  • LO2 Understand the models of spatial
    information
  • LO3 Understand the 3-step design of databases
  • Conceptual - ER model
  • Logical - Relational model
  • Physical
  • Translation from Conceptual to Logical
  • LO4 Learn about the trends in spatial data
    models
  • Mapping chapter sections to learning objectives
  • LO2 - 2.1
  • LO3 - 2.2
  • LO4 - 2.3, 2.4

20
2.2 Three-Step Database Design
  • Database applications are modeled using a
    three-step design process
  • Conceptual-datatypes,relationships and
    constraints(ER model)
  • Logical-mapping to a Relational model and
    associated query language(Relational Algebra)
  • Physical-file structures, indexing,
  • Scope
  • We discuss conceptual and logical data models in
    section 2.3
  • Physical model is discussed in chapter 4

21
Example Application Domain
  • Database design is for a specific application
    domain
  • Often a requirements document is available
  • Designers discuss requirements with end-users as
    needed
  • We will use a simple spatial application domain
  • to illustrate concepts in conceptual and logical
    data models
  • to illustrate translation of conceptual DM to
    logical DM
  • Spatial application domain
  • A state-park consists of forests.
  • A forest is a collection of forest-stands of
    different species
  • State-Park is accessed by roads and has a manager
  • State-Park has faciltities
  • River runs through state-park and supplies water
    to the facilities

22
2.2.1 Conceptual DM The ER Model
  • 3 basic concepts
  • Entities have an independent conceptual or
    physical existence.
  • Examples Forest, Road, Manager, ...
  • Entities are characterized by Attributes
  • Example Forest has attributes of name,
    elevation, etc.
  • An Entity interacts with another Entity through
    relationships.
  • Road allow access to Forest interiors.
  • This relationship may be name Accesses
  • Comparison with Object model of spatial
    information
  • Entities are collections of attributes are like
    objects
  • However ER model does not permit general user
    defined operations
  • Relationships are not directly supported in
    Object model
  • but may be simulated via operations

23
Relationship Types
  • Relationships can be categorized by
  • cardinality constraints
  • other properties, e.g. number of participating
    entities
  • Binary relationship two entities participate
  • Types of Cardinality constraints for binary
    relationships
  • One-One An instance of an entity relates to a
    unique instance of other entity.
  • Many-One Many instances of an entity relate to
    an instance of an other.
  • Many-Many Many instances of one entity relate to
    multiple instances of another.
  • Exercise Identify type of cardinality constraint
    for following
  • Many facilities belong to a forest. Each facility
    belong to one forest.
  • A manager manages 1 forest. Each forest has 1
    manager.
  • A river supplies water to many facilities. A
    facility gets water from many rivers.

24
ER Diagrams Graphical Notation
  • ER Diagrams are graphic representation of ER
    models
  • Several different graphic notation are used
  • We use a simple notation summarized below
  • Example ER Diagram for Forest exampl in next
    slide
  • Q? Compare and contrast Atributes and
    Multi-valued attributes.

Concept Symbol
Entities
Attributes
Multi-valued Attributes
Relationships
Cardinality of Relationship 11, M1, MN
25
ER Diagram for State-Park
Fig 2.4
  • Exercise
  • List the entities, attributes, relationships in
    this ER diagram
  • Identify cardinality constraint for each
    relationship.
  • How many roads Accesses a Forest_stand? (one
    or many)

26
2.2.2 Logical Data Model The Relational Model
  • Relational model is based on set theory
  • Main concepts
  • Domain a set of values for a simple attribute
  • Relation cross-product of a set of domains
  • Represents a table, i.e. homogeneous collection
    of rows (tuples)
  • The set of columns (i.e. attributes) are same for
    each row
  • Comparison to concepts in conceptual data model
  • Relations are similar to but not identical to
    entities
  • Domains are similar to attributes
  • Translation rules establishing exact
    correspondence are discussed in 2.2.3

27
Relational Schema
  • Schema of a Relation
  • Enumerates columns, identifies primary key and
    foreign keys.
  • Primary Key
  • one or more attributes uniquely identify each row
    within a table
  • Foreign keys
  • Rs attributes which form primary key of another
    relation S
  • Value of a foreign key in any tuple of R match
    values in some row of S
  • Relational schema of a database
  • collection of schemas of all relations in the
    database
  • Example Figure 2.5 (next slide)
  • Ablue print summary drawing of the database table
    structures
  • Allows analysis of storage costs, data
    redundancy, querying capabilities
  • Some databases were designed as relational schema
    in 1980s
  • Nowadays, databases are designed as E R models
    and relational schema is generated via CASE tools

28
Relational Schema Example
  • Exercise
  • Identify relations with
  • primary keys
  • foreign keys
  • other attributes
  • Compare with ER diagram
  • Figure 2.4, pp. 37

Fig 2.5
29
Relational Schema for Point, Line, Polygon
and Elevation
  • Relational model restricts attribute domains
  • simple atomic values, e.g. a number
  • Disallows complex values (e.g. polygons) for
    columns
  • Complex values need to be decomposed into simpler
    domains
  • A polygon may be decomposed into edges and
    vertices (Fig. 2.5)

Fig 2.5
30
More on Relational Model
  • Integrity Constraints
  • Key Every relation has a primary key.
  • Entity Integrity Value of primary key in a row
    is never undefined
  • Referential Integrity Value of an attribute of a
    Foreign Key must appear as a value in the primary
    key of another relationship or must be null.
  • Normal Forms (NF) for Relational schema
  • Reduce data redundancy and facilitate querying
  • 1st NF Each column in a relation contains an
    atomic value.
  • 2nd and 3rd NF Values of non-key attributes are
    fully determined by the values of the primary
    key, only the primary key, and nothing but the
    primary key.
  • Other normal forms exists but are seldom used
  • Translating a well-designed ER model yields a
    relational schema in 3rd NF
  • satisfying definition of 1st, 2nd and 3rd normal
    forms

31
2.2.3 Mapping ER to Relational
  • Highlights of transaltion rules (section 2.2.3)
  • Entity becomes Relation
  • Attributes become columns in the relation
  • Multi-valued attributes become a new relation
  • includes foreign key to link to relation for the
    entity
  • Relationships (11, 1N) become foreign keys
  • MN Relationships become a relation
  • containing foreign keys or relations from
    participating entities
  • Example and Exercise
  • Compare Fig. 2.4 and Fig. 2.5
  • Identify the relational schema components for
  • entity Facility, its attributes and its
    relationships
  • Note an empty relation box in Fig. 2.5. Fill in
    its schema.

32
Learning Objectives
  • Learning Objectives (LO)
  • LO1 Understand concept of data models
  • LO2 Understand the models of spatial
    information
  • LO3 Understand the 3-step design of databases
  • LO4 Learn about the trends in spatial data
    models
  • Pictograms in conceptual models
  • UML class diagrams
  • Mapping Sections to learning objectives
  • LO2 - 2.1
  • LO3 - 2.2
  • LO4 - 2.3, 2.4

33
2.3 Extending ER with Spatial Concepts
  • Motivation
  • ER Model is based on discrete sets with no
    implicit relationships
  • Spatial data comes from a continuous set with
    implicit relationships
  • Any pair of spatial entities has relationships
    like distance, direction,
  • Explicitly drawing all spatial relationship
  • clutters ER diagram
  • generates additional tables in relational schema
  • Misses implicit constraints in spatial
    relationships (e.g. partition)
  • Pictograms
  • Label spatial entities along with their spatial
    data types
  • Allows inference of spatial relationships and
    constraints
  • Reduces clutter in ER diagram and relational
    schema
  • Example Fig. 2.7 (next slide) is simpler than
    Fig. 2.4

34
ER Diagram with Pictograms An Example
Fig 2.7
35
Specifying Pictograms
  • Grammar based approach
  • Rewrite rule
  • like English syntax diagrams
  • Classes of pictograms
  • Entity pictograms
  • basic point, line, polygon
  • collection of basic
  • ...
  • Relationship pictograms
  • partition, network

36
Entity Pictograms Basic shapes, Collections
37
Entity Pictograms Derived and Alternate Shapes
  • Derived shape example is city center point from
    boundary polygon
  • Alternate shape example A road is represented as
    a polygon for construction
  • or as a line for navigation

38
2.4 Conceptual Data Modeling with UML
  • Motivation
  • ER Model does not allow user defined operations
  • Object oriented software development uses UML
  • UML stands for Unified Modeling Language
  • It is a standard consisting of several diagrams
  • class diagrams are most relevant for data
    modeling
  • UML class diagrams concepts
  • Attributes are simple or composite properties
  • Methods represent operations, functions and
    procedures
  • Class is a collection of attributes and methods
  • Relationship relate classes
  • Example UML class diagram Figure 2.8

39
UML Class Diagram with Pictograms Example
  • Exercise Identify classes, attributes, methods,
    relationships in Fig. 2.8.
  • Compare Fig. 2.8 with corresponding ER diagram in
    Fig. 2.7.

Fig 2.8
40
Comparing UML Class Diagrams to ER Diagrams
  • Concepts in UML class diagram vs. those in ER
    diagrams
  • Class without methods is an Entity
  • Attributes are common in both models
  • UML does not have key attributes and integrity
    constraints
  • ERD does not have methods
  • Relationships properties are richer in ERDs
  • Entities in ER diagram relate to datasets, but
    UML class diagram
  • can contain classes which have little to do with
    data

41
2.5 Summary
  • Spatial Information modeling can be classed into
    Field based and Object based
  • Field based for modeling smoothly varying
    entities, like rainfall
  • Object based for modeling discrete entities, like
    country

42
Summary
  • A data model is a high level description of the
    data
  • it can help in early analysis of storage cost,
    data quality
  • There are two popular models of spatial
    information
  • Field based and Object based
  • Database are designed in 3-steps
  • Conceptual, Logical and Physical
  • Pictograms can simplify Conceptual data models
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